國立清華大學 數學系

Abstract: The Heisenberg group, as Euclidean space, is a kind of Klein geometry.We will consider the Heisenberg group as a pseudohermitian manifold.The symmetry group is hence the group consisting of those diffeomorphisms preserving the standard pseudohermitian structure.A fundamental problem in Klein geometry is to ask when two submanifolds are congruent with each other. In order to solve the problem, we will introduce a complete set of invariants for hypersurfaces in the Heisenberg groups.Our method is the Cartan's moving frame method and calculus on Lie groups. Finally, if time is enough, I would like to introduce somethings relatedwith contact topology. Tea Time: 3:30PM, R707